total 28375took 0.15s

Multiple Independent Subspace ClusteringsMay 10 2019Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it's still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this process, we ... More

Multi-View Multiple ClusteringMay 13 2019Multiple clustering aims at exploring alternative clusterings to organize the data into meaningful groups from different perspectives. Existing multiple clustering algorithms are designed for single-view data. We assume that the individuality and commonality ... More

Weakly-paired Cross-Modal HashingMay 29 2019Hashing has been widely adopted for large-scale data retrieval in many domains, due to its low storage cost and high retrieval speed. Existing cross-modal hashing methods optimistically assume that the correspondence between training samples across modalities ... More

ActiveHNE: Active Heterogeneous Network EmbeddingMay 14 2019Heterogeneous network embedding (HNE) is a challenging task due to the diverse node types and/or diverse relationships between nodes. Existing HNE methods are typically unsupervised. To maximize the profit of utilizing the rare and valuable supervised ... More

Multi-View Multi-Instance Multi-Label Learning based on Collaborative Matrix FactorizationMay 13 2019Multi-view Multi-instance Multi-label Learning(M3L) deals with complex objects encompassing diverse instances, represented with different feature views, and annotated with multiple labels. Existing M3L solutions only partially explore the inter or intra ... More

Ranking-based Deep Cross-modal HashingMay 11 2019Cross-modal hashing has been receiving increasing interests for its low storage cost and fast query speed in multi-modal data retrievals. However, most existing hashing methods are based on hand-crafted or raw level features of objects, which may not ... More

ActiveHNE: Active Heterogeneous Network EmbeddingMay 14 2019May 15 2019Heterogeneous network embedding (HNE) is a challenging task due to the diverse node types and/or diverse relationships between nodes. Existing HNE methods are typically unsupervised. To maximize the profit of utilizing the rare and valuable supervised ... More

Multi-View Multi-Instance Multi-Label Learning based on Collaborative Matrix FactorizationMay 13 2019May 15 2019Multi-view Multi-instance Multi-label Learning(M3L) deals with complex objects encompassing diverse instances, represented with different feature views, and annotated with multiple labels. Existing M3L solutions only partially explore the inter or intra ... More

A well-balanced reconstruction for wetting/drying frontsDec 11 2014In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction ... More

Conditional Adversarial Synthesis of 3D Facial Action UnitsFeb 21 2018Mar 15 2018Employing deep learning-based approaches for fine-grained facial expression analysis, such as those involving the estimation of Action Unit (AU) intensities, is difficult due to the lack of a large-scale dataset of real faces with sufficiently diverse ... More

Real-time 3D Face-Eye Performance Capture of a Person Wearing VR HeadsetJan 21 2019Teleconference or telepresence based on virtual reality (VR) headmount display (HMD) device is a very interesting and promising application since HMD can provide immersive feelings for users. However, in order to facilitate face-to-face communications ... More

Surgery on links with unknotted components and three-manifoldsJan 22 2008It is shown that any closed three-manifold M obtained by integral surgery on a knot in the three-sphere can always be constructed from integral surgeries on a 3-component link L with each component being an unknot in the three-sphere. It is also interesting ... More

Cluster categories for marked surfaces: punctured caseOct 31 2013Jan 08 2017We study the cluster categories arising from marked surfaces (with punctures and non-empty boundaries). By constructing skewed-gentle algebras, we show that there is a bijection between tagged curves and string objects. Applications include interpreting ... More

Asymptotic properties of one-step $M$-estimators based on nonidentically distributed observations with applications to nonlinear regression problemsMar 11 2015Apr 11 2016We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These estimators ... More

Decorated marked surfaces II: Intersection numbers and dimensions of HomsNov 14 2014May 28 2015We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface $\mathbf{S}_\bigtriangleup$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection ... More

Finite presentations for spherical/braid twist groups from decorated marked surfacesMar 29 2017Oct 29 2018We give a finite presentation for the braid twist group of a decorated surface. If the decorated surface arises from a triangulated marked surface without punctures, we obtain a finite presentation for the spherical twist group of the associated 3-Calabi-Yau ... More

Displacement induced electric force and natural self-oscillation of a free electronApr 13 2013Jun 13 2013We show that a kind of displacement induced temporary electric force of a single point charge can be derived by using Maxwell stress analysis. This force comes from the variation of the charge's electric intensities that follow Coulomb's inverse square ... More

Decorated marked surfaces II: Intersection numbers and dimensions of HomsNov 14 2014Jun 02 2017We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface $\mathbf{S}_\bigtriangleup$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection ... More

Introduction to renormalizationJun 06 2006In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural disorder, frustrations. ... More

A central limit theorem for fluctuations in one dimensional stochastic homogenizationAug 20 2015In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with additive spatial ... More

Integrable systems associated with generalized Sklyanin algebraDec 28 2008Using the point fusion procedure we obtain the new integrable systems from the Elliptic Schlesinger system (ESS). These new systems have the pole orders higher than one in the matrix of the Lax operator. Quadratic Poisson algebras on the phase space of ... More

Nonlinear variable selection with continuous outcome: a nonparametric incremental forward stagewise approachJan 20 2016Mar 25 2016We present a method of variable selection for the situation where some predictors are nonlinearly associated with a continuous outcome variable. The method doesn't assume any specific functional form, and can select from a large number of candidates. ... More

2-Selmer near-companion curvesOct 04 2016Let $E$ and $A$ be elliptic curves over a number field $K$. Let $\chi$ be a quadratic character of $K$. We prove the conjecture posed by Mazur and Rubin on $n$-Selmer near-companion curves in the case $n=2$. Namely, we show if the difference of the $2$-Selmer ... More

The Discord-like Correlation of Bipartite CoherenceNov 01 2016Quantum discord is a measure of quantum correlation by the the mutual information difference between the state and the output state after the local von Neumann measurement, where the mutual information contained in a bipartite state is defined as the ... More

Some Simulation Results for Emphatic Temporal-Difference Learning AlgorithmsMay 06 2016This is a companion note to our recent study of the weak convergence properties of constrained emphatic temporal-difference learning (ETD) algorithms from a theoretic perspective. It supplements the latter analysis with simulation results and illustrates ... More

The Scalar Curvature Deformation Equation on Locally Conformally Flat ManifoldsMar 20 2007We study the equation $\Delta_g u -\frac{n-2}{4(n-1)}R(g)u+Ku^p=0 (1+\zeta \leq p \leq \frac{n+2}{n-2})$ on locally conformally flat compact manifolds $(M^n,g)$. We prove the following: (i) When the scalar curvature $R(g)>0$ and the dimension $n \geq ... More

QND and higher order effects for a nonlinear meter in an interferometric gravitational wave antennaMar 01 1997A new optical topology and signal readout strategy for a laser interferometer gravitational wave detector were proposed recently by Braginsky and Khalili . Their method is based on using a nonlinear medium inside a microwave oscillator to detect the gravitational-wave-induced ... More

On generalized trigonometric functions and series of rational functionsOct 15 2016Here we introduce a way to construct generlized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$. We will show that those generalized trigonometric ... More

An improved helical subgrid-scale model and large-eddy simulation methods in helical turbulenceAug 12 2014For helical isotropic turbulence, an improved two-term helical subgrid-scale (SGS) model is proposed and four types of dynamic methods are given to do large-eddy simulation (LES), which include the standard dynamic procedure, the least quatratic sum dynamic ... More

Negativity of Perelman's Li-Yau-Hamilton type expressionOct 03 2008Chau-Tam-Yu has proved the non-positivity of Perelman's new Li-Yau-Hamilton type expression on noncompact manifolds. In this article, we further prove that $v$ is negative if the Ricci flow is not end up with an Euclidean space.

A geometric proof of the classification of complex vector cross productOct 03 2008In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.

Hessian comparison and eigenvalue estimate of almost Hermitian manifoldsSep 26 2012In this paper, by using the Bochner technique on almost Hermitian manifolds, we obtain a complex Hessian comparison for almost Hermitian manifolds generalizing the Laplacian comparison for almost Hermitian manifolds by Tossati, and reprove a diameter ... More

Global well-posedness for the two dimensional Navier-Stokes-Vlasov EquationsJul 19 2012Oct 11 2012The global well-posedness for the incompressible Navier-Stokes-Vlasov equations in two spatial dimensions is established by a priori estimates, the characteristic method and the semigroup analysis.

Interacting scale but non-conformal field theoriesNov 30 2016There is a dilemma in constructing interacting scale invariant but not conformal invariant Euclidean field theories. On one hand, scale invariance without conformal invariance seems more generic by requiring only a smaller symmetry. On the other hand, ... More

Hearts of cotorsion pairs are functor categories over coheartsApr 21 2015Jan 18 2016We study hearts of cotorsion pairs in triangulated and exact categories.We give a sufficient and necessary condition when the hearts have enough projectives. We also show in such condition they are equivalent to functor categories over cohearts of the ... More

Constant Factor Time Optimal Multi-Robot Routing on High-Dimensional Grids in Mostly Sub-Quadratic TimeJan 31 2018Let $G = (V, E)$ be an $m_1 \times \ldots \times m_k$ grid. Assuming that each $v \in V$ is occupied by a robot and a robot may move to a neighboring vertex in a step via synchronized rotations along cycles of $G$, we first establish that the arbitrary ... More

Principal Postnikov towers and TQ localization of structured ring spectraFeb 09 2019The aim of this paper is to establish that every (-1)-connected algebra over a spectral operad O is TQ-local, in the sense that the natural coaugmentation map to its topological Quillen localization (this can be thought of as the part of the O-algebra ... More

Folding quivers and numerical stability conditionsSep 30 2012We generalize Deng-Du's folding argument, for the bounded derived category D(Q) of an acyclic quiver Q, to the finite dimensional derived category D(Gamma Q) of the Ginzburg algebra Gamma Q associated to Q. We show that the F-stable category of D(Gamma ... More

Evolution of massive binary black holesSep 27 2001Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper, we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques ... More

Stellar collisions in galactic centers: black hole growth and color gradientsOct 12 2002We study the effects of stellar collisions, particularly on feeding massive black holes (BHs) and color gradients, in realistic galactic centers. We find that the mass released by stellar collisions is not sufficient to account for the present BH mass ... More

Gaussian fluctuations of the 2D KPZ equationDec 18 2018We prove the 2D KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards-Wilkinson equation with an effective variance.

Primality tests for Fermat numbers and 2^(2k+1)\pm2^(k+1)+1Dec 10 2009Robert Denomme and Gordan Savin made a primality test for Fermat numbers 2^(2^k)+1 using elliptic curves. We propose another primality test using elliptic curves for Fermat numbers and also give primality tests for integers of the form 2^(2k+1)\pm2^(k+1)+1. ... More

Strict entanglement monotonicity under local operations and classical communicationApr 02 2019Entanglement monotone is defined as a convex measure of entanglement that does not increase on average under local operations and classical communication (LOCC). Here we call an entanglement monotone a strict entanglement monotone (SEM) if it decreases ... More

A quantum homomorphic encryption scheme for polynomial-sized circuitsOct 02 2018Apr 04 2019Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program ... More

From Composite Fermions to Calogero-Sutherland Model: Edge of Fractional Quantum Hall Liquid and the Dimension ReductionNov 04 1999We derive a microscopic model describing the low-lying edge excitations in the fractional quantum Hall liquid with $\nu=\frac{\nu^*} {\tilde\phi\nu^*+1}$. For $\nu^*>0$, it is found that the composite fermion model reduces to an SU$(\nu^*)$ Calogero-Sutherland ... More

On irreducible partials of Ricci tensor traceless part in finite space-time region in GRMar 25 2003Riemann tensor irreducible part $E_{iklm} = {1/2} (g_{il}S_{km} + g_{km}S_{il} - g_{im}S_{kl} - g_{kl}S_{im})$ constructed from metric tensor $g_{ik}$ and traceless part of Ricci tensor $S_{ik} = R_{ik} - {1/4} g_{ik} R$ is expanded into bilinear combinations ... More

Freeness of $p$-adically Completed Modular Jacobians over a Hecke AlgebraApr 11 2019We construct a Taylor-Wiles system using a family of $p$-adically completed modular Jacobians over suitable Hecke algebras and prove that certain $p$-adically completed Mordell-Weil groups of these Jacobians is free of finite rank over a Hecke algebra. ... More

The integral geometric Satake equivalence in mixed characteristicMar 26 2019Let $k$ be an algebraically closed field of characteristic $p$. Denote by $W(k)$ the ring of Witt vectors of $k$. Let $F$ denote a totally ramified finite extension of $W(k)[1/p]$ and $\mathcal{O}$ the its ring of integers. For a connected reductive group ... More

CM Values of Green Functions Associated to Special Cycles on Shimura Varieties with Applications to Siegel 3-Fold $X_2(2)$Oct 10 2017Aug 29 2018We generalize the definition of CM cycles beyond the small and big CM ones studied by various authors and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts. ... More

A General Method for Large Eddy Simulation in Different Range of Turbulent FlowsDec 12 2012Aug 15 2014Traditional large eddy simulation is based on Kolmogrov's hypothesis, and done in the inertial range. In inertial range the LES model coefficient is scale-invariant. In many cases, such as computing in the boundary layer, the filter scale is not in the ... More

Gossamer supercoductivity and the mean field approximation of a new effective Hubbard modelNov 07 2002Nov 08 2002We construct a new effective two-dimensional Hubbard model by taking the different electron occupancy on site into account. The mean field state of the new Hamiltonian gives rise to the gossamer superconducting state proposed by Laughlin recently(cond-mat/0209269). ... More

A Quantity Characterising Variation of Observed Magnetic Twist of Solar Active RegionsDec 21 2017An alternative parameter $R_{J_z}$ is introduced as the ratio of one of two kinds of opposite-sign current to the total current and investigate the relationship between the quantity and the hemispheric sign rule of helicity (HSR) that is established by ... More

A remark on degenerate singularity in three dimensional Ricci flowSep 05 2007We show that a rescale limit at any degenerate singularity of Ricci flow in dimension 3 is a steady gradient soliton. In particular, we give a geometric description of type I and type II singularities.

Consistency of local renormalization group in d=3Jul 30 2013We discuss Weyl anomaly and consistency conditions of local renormalization group in d=1+2 dimensional quantum field theories. We give a classification of the consistency conditions and ambiguities in most generality within the power-counting renormalization ... More

Supercurrent, Supervirial and SuperimprovementAug 23 2012Nov 15 2014Supersymmetric field theories possess a rich structure in their supercurrent supermultiplets. Some symmetries are manifest in one supercurrent supermultiplet but not in the others; for instance, R-symmetry is manifest in the R-multiplet but not in the ... More

Superfield Formulation for Non-Relativistic Chern-Simons-Matter TheoryFeb 13 2009We construct a superfield formulation for non-relativistic Chern-Simons-Matter theories with manifest dynamical supersymmetry. By eliminating all the auxiliary fields, we show that the simple action reduces to the one obtained by taking non-relativistic ... More

SUSY Unparticle and Conformal SequesteringJul 17 2007Jul 18 2007We investigate unparticle physics with supersymmetry (SUSY). The SUSY breaking effects due to the gravity mediation induce soft masses for the SUSY unparticles and hence break the conformal invariance. The unparticle physics observable in near future ... More

Index for Orbifold Quiver Gauge TheoriesDec 22 2005Mar 22 2006We compute the index for orbifold quiver gauge theories. We compare it with the results obtained from the type IIB supergravity (superstring) on AdS_5 \times S^5/\Gamma.

Holographic interpretation of renormalization group approach to singular perturbations in non-linear differential equationsMay 17 2013May 29 2013We give a holographic explanation how the renormalization group approach to singular perturbations in non-linear differential equations proposed by Chen, Goldenfeld and Oono is indeed equivalent to a renormalization group method in quantum field theories ... More

Intrinsic ambiguity in second order viscosity parameters in relativistic hydrodynamicsJun 12 2012We show that relativistic hydrodynamics in Minkowski space-time has intrinsic ambiguity in second order viscosity parameters in the Landau-Lifshitz frame. This stems from the possibility of improvements of energy-momentum tensor. There exist at least ... More

Comments on scale invariant but non-conformal supersymmetric field theoriesSep 27 2011We investigate a possibility of scale invariant but non-conformal supersymmetric field theories from a perturbative approach. The explicit existence of monotonically decreasing a-function that generates beta-functions as a gradient flow provides a strong ... More

Heavy-quark recombination in Z^0 decayAug 28 2003We briefly review the recent advances of heavy-quark recombination mechanism. This mechanism predicts a class of power-suppressed 3-jet events in $Z^0$ decay, such as $b\bar{b}q$ and $b\bar{b}\bar{q}$. Furthermore, heavy quark fragmentation function also ... More

A Liouville property of holomorphic mapsMar 04 2010In this article, we prove a Liouville property of holomorphic maps from a complete Kahler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kahler manifold with a certain assumption on the sectional curvature.

On the dimension datum of a subgroup. IIMar 16 2018This paper studies three aspects around dimension datum: (1), a generalization of the dimension datum, which we call the tau-dimension datum; (2), dimension data of disconnected subgroups; (3), compactness of isospectral sets of normal homogeneous spaces. ... More

Invariance of the Gibbs measure for the Benjamin-Ono equationOct 04 2012In this paper we consider the periodic Benjemin-Ono equation. We will establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [20]. As an intermediate step, we also obtain a local well-posedness ... More

On dually flat Randers metricsSep 06 2012In this paper, I will show how to use beta-deformations to deal with dual flatness of Randers metrics. beta-deformations is a new method in Riemann-Finsler geometry, it is introduced by the author(see arxiv:1209.0845). Later on I will provide more applications ... More

Quantum Boson Algebra and Poisson Geometry of the Flag VarietyApr 23 2019In his work on crystal bases \cite{Kas}, Kashiwara introduced a certain degeneration of the quantized universal enveloping algebra of a semi-simple Lie algebra $\mathfrak g$, which he called a quantum boson algebra. In this paper, we construct Kashiwara ... More

Acrobot Swing Up with MATLABJan 13 2019This note presents a solution of the swing-up task of two acrobots using trajectory optimization method. The equations of motion for 2-link and 3-link acrobot are manually derived, and then form the dynamics of the robots. Numerical integration method ... More

Infinite horizon jump-diffusion forward-backward stochastic differential equations and their application to backward linear-quadratic problemsAug 19 2016In this paper, we investigate infinite horizon jump-diffusion forward-backward stochastic differential equations under some monotonicity conditions. We establish an existence and uniqueness theorem, two stability results and a comparison theorem for solutions ... More

A Thermodynamic Picture of Financial Market and Model RiskMar 30 2019By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused by model uncertainty ... More

Harmonic Summing Improves Pulsar Detection Sensitivity: A Probability AnalysisNov 17 2018Practical application of the harmonic summing technique in the power-spectrum analysis for searching pulsars has exhibited the technique's effectiveness. In this paper, theoretical verification of harmonic summing considering power's noise-signal probability ... More

Glitches detected in southern radio pulsarsNov 09 2012Parkes pulse arrival-time data for 165 radio pulsars spanning from 1990 to 2011 have been searched for period glitches. Forty-six events out of the detected 107 glitches were found to be new contributions to the entire glitch population which currently ... More

On Conditional CorrelationsNov 09 2018May 26 2019The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional versions to ... More

On the maximal number of exceptional values of Gauss maps for various classes of surfacesMay 22 2012Nov 10 2012The main goal of this paper is to reveal the geometric meaning of the maximal number of exceptional values of Gauss maps for several classes of immersed surfaces in space forms, for example, complete minimal surfaces in the Euclidean three-space, weakly ... More

Function-theoretic properties for the Gauss maps of various classes of surfacesNov 08 2013May 28 2014We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the ... More

Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrationsAug 07 2014Oct 11 2016Inspired by Katz-Mazur theorem on crystalline cohomology and by Eskin-Kontsevich-Zorich's numerical experiments, we conjecture that the polygon of Lyapunov spectrum lies above (or on) the Harder-Narasimhan polygon of the Hodge bundle over any Teichm\"uller ... More

Blowup rate control for solution of Jang's equation and its application on Penrose inequalityJun 20 2019We prove that the blowup term of a blowup solution of Jang's equation on an initial data set (M,g,k) near an arbitrary strictly stable MOTS $ \Sigma $ is exactly $ -\frac{1}{\sqrt{\lambda}}\log \tau $, where $ \tau $ is the distance from $ \Sigma $ and ... More

Reconstruction of Binary Functions and Shapes from Incomplete Frequency InformationApr 04 2011Mar 12 2012The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization problem. We further ... More

On Markov Decision Processes with Borel Spaces and an Average Cost CriterionJan 10 2019We consider average-cost Markov decision processes (MDPs) with Borel state and action spaces and universally measurable policies. For the nonnegative cost model and an unbounded cost model, we introduce a set of conditions under which we prove the average ... More

Hopf-Galois objects of Calabi-Yau Hopf algebrasNov 28 2015By using the language of cogroupoids, we show that Hopf-Galois objects of a twisted Calabi-Yau Hopf algebra with bijective antipode are still twisted Calabi-Yau, and give their Nakayama automorphism explicitly. As applications, cleft Galois objects of ... More

An Explicit Example Of Optimal Portfolio-Consumption Choices With Habit Formation And Partial ObservationsDec 13 2011Aug 11 2014We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only observing the market ... More

Generalized Strichartz Estimates on Perturbed Wave Equation and Applications on Strauss ConjectureMay 01 2009Jan 26 2011In this paper we show a general Strichartz estimate for certain perturbed wave equation, and here we can drop the nontrapping hypothesis and handle trapping obstacles with some loss of derivatives for data in the local energy decay estimates. Then we ... More

Liouville Type Theorem for Some Nonlocal Elliptic EquationsJun 12 2017In this paper, we prove some Liouville theorem for the following elliptic equations involving nonlocal nonlinearity and nonlocal boundary value condition $$ \left\{ \begin{array}{ll} \displaystyle -\Delta u(y)=\intpr \frac{ F(u(x',0))}{|(x',0)-y|^{N-\alpha}}dx'g(u(y)), ... More

On Linear Programming for Constrained and Unconstrained Average-Cost Markov Decision Processes with Countable Action Space and Strictly Unbounded CostsMay 28 2019We consider the linear programming approach for constrained and unconstrained Markov decision processes (MDPs) with the long-run average cost criterion, where the class of MDPs in our study have a Borel state space and a discrete, countable action space. ... More

A phase transformation for the number of optimal paths in first passage percolationMay 30 2019We consider the first passage percolation model on the square lattice with an edge weight distribution F. In this paper, we consider the number of optimal paths for two points separated by a long distance. We show that there is a phase transition in the ... More

Abelian quotients associated with fully rigid subcategoriesFeb 20 2019In this article, we study the Gorenstein property of abelian quotient categories induced by fully rigid subcategories on an exact category B. We also study when d-cluster tilting subcategories become fully rigid. We show that the quotient abelian category ... More

On slightly degenerate fusion categoriesMar 15 2019Mar 21 2019In this paper, we first show for a slightly degenerate pre-modular fusion category $\mathcal{C}$ that squares of dimensions of simple objects divide half of the dimension of $\mathcal{C}$, and that slightly degenerate fusion categories of FP-dimensions ... More

Tropicalizing the positive semidefinite coneSep 24 2013We study the tropicalization of the cone of positive semidefinite matrices over the ordered field of real Puiseux series. The tropical PSD matrices form the normal cone of the Newton polytope of the symmetric determinant at the vertex corresponding to ... More

Coupling between the 45 Hz Horizontal-Branch Oscillation and the Normal Branch Oscillation in Scorpius X-1Mar 08 2007The observations of the bright persistent neutron star low-mass X-ray binary (LMXB) Sco X-1 performed with the {\it Rossi X-ray Timing Explorer} (RXTE) show a $\sim$ 6 Hz normal-branch oscillation (NBO), a $\sim$ 45 Hz horizontal-branch oscillation (HBO), ... More

Global dimension function, Gepner equations and $q$-stability conditionsJun 29 2018Dec 04 2018We study the global dimension function $\operatorname{gl.dim}\colon\mathbb{C}\backslash\operatorname{Stab}\mathcal{D}/\operatorname{Aut}\to\mathbb{R}_{\ge0}$ on the quotient space of Bridgeland's stability conditions on a triangulated category $\mathcal{D}$ ... More

Topological structure of spaces of stability conditions and topological Fukaya type categoriesMay 31 2018Jul 06 2018This is a survey on two closely related subjects. First, we review the study of topological structure of `finite type' components of spaces of Bridgeland's stability conditions on triangulated categories. The key is to understand Happel-Reiten-Smalo tilting ... More

The braid group for a quiver with superpotentialDec 27 2017Feb 24 2018We survey and compare various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with A.~King. Our motivations come from the study of cluster algebras, Calabi-Yau ... More

C-sortable words as green mutation sequencesApr 30 2012May 26 2015Let $Q$ be an acyclic quiver and $\mathbf{s}$ be a sequence with elements in the vertex set $Q_0$. We describe an induced sequence of simple (backward) tilting in the bounded derived category $\mathcal{D}(Q)$, starting from the standard heart $\mathcal{H}_Q=\operatorname{mod}\mathbf{k}Q$ ... More

Stability conditions and quantum dilogarithm identities for Dynkin quiversNov 03 2011Nov 03 2014We study fundamental group of the exchange graphs for the bounded derived category D(Q) of a Dynkin quiver Q and the finite-dimensional derived category D(\Gamma_N Q) of the Calabi-Yau-N Ginzburg algebra associated to Q. In the case of D(Q), we prove ... More

Conformal Contact Terms and Semi-Local TermsJun 19 2019Jul 01 2019We study conformal properties of local terms such as contact terms and semi-local terms in correlation functions of a conformal field theory. Not all of them are universal observables but they do appear in physically important correlation functions such ... More

Conformal equations that are not Virasoro or Weyl invariantFeb 14 2019Feb 27 2019While the argument by Zamolodchikov and Polchinski suggests global conformal invariance implies Virasoro invariance in two-dimensional unitary conformal field theories with discrete dilatation spectrum, it is not the case in more general situations without ... More

Gravity Dual for Very Special Conformal Field Theories in type IIB SupergravityJul 24 2018We study holographic dual descriptions of very special conformal field theories with the T(2) symmetry. After constructing solutions in effective five dimensional Einstein gravity coupled with massive two-form fields, we uplift them to the ten dimensional ... More

Bootstrap experiments on higher dimensional CFTsMay 08 2017Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal bootstrap equations. ... More

Interacting scale but non-conformal field theoriesNov 30 2016Dec 13 2016There is a dilemma in constructing interacting scale invariant but not conformal invariant Euclidean field theories. On one hand, scale invariance without conformal invariance seems more generic by requiring only a smaller symmetry. On the other hand, ... More

Very Special Conformal Field Theories (VSCFT) and their holographic dualsJul 18 2017Feb 19 2018Cohen and Glashow introduced the notion of very special relativity as viable space-time symmetry of elementary particle physics. As a natural generalization of their idea, we study the subgroup of the conformal group, dubbed very special conformal symmetry, ... More